pgr_bellmanFord  Experimental
¶
pgr_bellmanFord
— Shortest path(s) using BellmanFord algorithm.
Warning
Possible server crash
These functions might create a server crash
Warning
Experimental functions
They are not officially of the current release.
They likely will not be officially be part of the next release:
The functions might not make use of ANYINTEGER and ANYNUMERICAL
Name might change.
Signature might change.
Functionality might change.
pgTap tests might be missing.
Might need c/c++ coding.
May lack documentation.
Documentation if any might need to be rewritten.
Documentation examples might need to be automatically generated.
Might need a lot of feedback from the comunity.
Might depend on a proposed function of pgRouting
Might depend on a deprecated function of pgRouting
Availability
Version 3.2.0
New experimental signature:
pgr_bellmanFord
(Combinations)
Version 3.0.0
New experimental signatures:
pgr_bellmanFord
(One to One)pgr_bellmanFord
(One to Many)pgr_bellmanFord
(Many to One)pgr_bellmanFord
(Many to Many)
Description¶
BellmanFord’s algorithm, is named after Richard Bellman and Lester Ford, who
first published it in 1958 and 1956, respectively.It is a graph search algorithm
that computes shortest paths from a starting vertex (start_vid
) to an ending
vertex (end_vid
) in a graph where some of the edge weights may be negative.
Though it is more versatile, it is slower than Dijkstra’s algorithm.This
implementation can be used with a directed graph and an undirected graph.
 The main characteristics are:
Process is valid for edges with both positive and negative edge weights.
Values are returned when there is a path.
When the start vertex and the end vertex are the same, there is no path. The agg_cost would be \(0\).
When the start vertex and the end vertex are different, and there exists a path between them without having a negative cycle. The agg_cost would be some finite value denoting the shortest distance between them.
When the start vertex and the end vertex are different, and there exists a path between them, but it contains a negative cycle. In such case, agg_cost for those vertices keep on decreasing furthermore, Hence agg_cost can’t be defined for them.
When the start vertex and the end vertex are different, and there is no path. The agg_cost is \(\infty\).
For optimization purposes, any duplicated value in the start_vids or end_vids are ignored.
The returned values are ordered:
start_vid ascending
end_vid ascending
Running time: \(O( start\_vids  * ( V * E))\)
Signatures¶
Summary
directed
])directed
])directed
])directed
])(seq, path_seq, [start_vid], [end_vid], node, edge, cost, agg_cost)
One to One¶
directed
])(seq, path_seq, node, edge, cost, agg_cost)
 Example:
From vertex \(6\) to vertex \(10\) on a directed graph
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edges',
6, 10, true);
seq  path_seq  node  edge  cost  agg_cost
+++++
1  1  6  4  1  0
2  2  7  8  1  1
3  3  11  9  1  2
4  4  16  16  1  3
5  5  15  3  1  4
6  6  10  1  0  5
(6 rows)
One to Many¶
directed
])(seq, path_seq, end_vid, node, edge, cost, agg_cost)
 Example:
From vertex \(6\) to vertices \(\{ 10, 17\}\) on a directed graph
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edges',
6, ARRAY[10, 17]);
seq  path_seq  end_vid  node  edge  cost  agg_cost
++++++
1  1  10  6  4  1  0
2  2  10  7  8  1  1
3  3  10  11  9  1  2
4  4  10  16  16  1  3
5  5  10  15  3  1  4
6  6  10  10  1  0  5
7  1  17  6  4  1  0
8  2  17  7  8  1  1
9  3  17  11  11  1  2
10  4  17  12  13  1  3
11  5  17  17  1  0  4
(11 rows)
Many to One¶
directed
])(seq, path_seq, start_vid, node, edge, cost, agg_cost)
 Example:
From vertices \(\{6, 1\}\) to vertex \(17\) on a directed graph
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[6, 1], 17);
seq  path_seq  start_vid  node  edge  cost  agg_cost
++++++
1  1  1  1  6  1  0
2  2  1  3  7  1  1
3  3  1  7  8  1  2
4  4  1  11  11  1  3
5  5  1  12  13  1  4
6  6  1  17  1  0  5
7  1  6  6  4  1  0
8  2  6  7  8  1  1
9  3  6  11  11  1  2
10  4  6  12  13  1  3
11  5  6  17  1  0  4
(11 rows)
Many to Many¶
directed
])(seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
 Example:
From vertices \(\{6, 1\}\) to vertices \(\{10, 17\}\) on an undirected graph
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[6, 1], ARRAY[10, 17],
directed => false);
seq  path_seq  start_vid  end_vid  node  edge  cost  agg_cost
+++++++
1  1  1  10  1  6  1  0
2  2  1  10  3  7  1  1
3  3  1  10  7  4  1  2
4  4  1  10  6  2  1  3
5  5  1  10  10  1  0  4
6  1  1  17  1  6  1  0
7  2  1  17  3  7  1  1
8  3  1  17  7  8  1  2
9  4  1  17  11  11  1  3
10  5  1  17  12  13  1  4
11  6  1  17  17  1  0  5
12  1  6  10  6  2  1  0
13  2  6  10  10  1  0  1
14  1  6  17  6  4  1  0
15  2  6  17  7  8  1  1
16  3  6  17  11  11  1  2
17  4  6  17  12  13  1  3
18  5  6  17  17  1  0  4
(18 rows)
Combinations¶
(seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
 Example:
Using a combinations table on an undirected graph.
The combinations table:
SELECT source, target FROM combinations;
source  target
+
5  6
5  10
6  5
6  15
6  14
(5 rows)
The query:
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edges',
'SELECT source, target FROM combinations',
false);
seq  path_seq  start_vid  end_vid  node  edge  cost  agg_cost
+++++++
1  1  5  6  5  1  1  0
2  2  5  6  6  1  0  1
3  1  5  10  5  1  1  0
4  2  5  10  6  2  1  1
5  3  5  10  10  1  0  2
6  1  6  5  6  1  1  0
7  2  6  5  5  1  0  1
8  1  6  15  6  2  1  0
9  2  6  15  10  3  1  1
10  3  6  15  15  1  0  2
(10 rows)
Parameters¶
Column 
Type 
Description 


Edges SQL as described below 


Combinations SQL as described below 

start vid 

Identifier of the starting vertex of the path. 
start vids 

Array of identifiers of starting vertices. 
end vid 

Identifier of the ending vertex of the path. 
end vids 

Array of identifiers of ending vertices. 
Optional parameters¶
Column 
Type 
Default 
Description 





Inner Queries¶
Edges SQL¶
Column 
Type 
Default 
Description 


ANYINTEGER 
Identifier of the edge. 


ANYINTEGER 
Identifier of the first end point vertex of the edge. 


ANYINTEGER 
Identifier of the second end point vertex of the edge. 


ANYNUMERICAL 
Weight of the edge ( 


ANYNUMERICAL 
1 
Weight of the edge (

Where:
 ANYINTEGER:
SMALLINT
,INTEGER
,BIGINT
 ANYNUMERICAL:
SMALLINT
,INTEGER
,BIGINT
,REAL
,FLOAT
Combinations SQL¶
Parameter 
Type 
Description 


ANYINTEGER 
Identifier of the departure vertex. 

ANYINTEGER 
Identifier of the arrival vertex. 
Where:
 ANYINTEGER:
SMALLINT
,INTEGER
,BIGINT
Return columns¶
Returns set of (seq, path_seq [, start_vid] [, end_vid], node, edge, cost,
agg_cost)
Column 
Type 
Description 



Sequential value starting from 1. 


Relative position in the path. Has value 1 for the beginning of a path. 


Identifier of the starting vertex. Returned when multiple starting vetrices are in the query. 


Identifier of the ending vertex. Returned when multiple ending vertices are in the query. 


Identifier of the node in the path from 


Identifier of the edge used to go from 


Cost to traverse from 


Aggregate cost from 
Additional Examples¶
 Example 1:
Demonstration of repeated values are ignored, and result is sorted.
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
seq  path_seq  start_vid  end_vid  node  edge  cost  agg_cost
+++++++
1  1  7  10  7  8  1  0
2  2  7  10  11  9  1  1
3  3  7  10  16  16  1  2
4  4  7  10  15  3  1  3
5  5  7  10  10  1  0  4
6  1  7  15  7  8  1  0
7  2  7  15  11  9  1  1
8  3  7  15  16  16  1  2
9  4  7  15  15  1  0  3
10  1  10  7  10  5  1  0
11  2  10  7  11  8  1  1
12  3  10  7  7  1  0  2
13  1  10  15  10  5  1  0
14  2  10  15  11  9  1  1
15  3  10  15  16  16  1  2
16  4  10  15  15  1  0  3
17  1  15  7  15  3  1  0
18  2  15  7  10  2  1  1
19  3  15  7  6  4  1  2
20  4  15  7  7  1  0  3
21  1  15  10  15  3  1  0
22  2  15  10  10  1  0  1
(22 rows)
 Example 2:
Making start vids the same as end vids.
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
seq  path_seq  start_vid  end_vid  node  edge  cost  agg_cost
+++++++
1  1  7  10  7  8  1  0
2  2  7  10  11  9  1  1
3  3  7  10  16  16  1  2
4  4  7  10  15  3  1  3
5  5  7  10  10  1  0  4
6  1  7  15  7  8  1  0
7  2  7  15  11  9  1  1
8  3  7  15  16  16  1  2
9  4  7  15  15  1  0  3
10  1  10  7  10  5  1  0
11  2  10  7  11  8  1  1
12  3  10  7  7  1  0  2
13  1  10  15  10  5  1  0
14  2  10  15  11  9  1  1
15  3  10  15  16  16  1  2
16  4  10  15  15  1  0  3
17  1  15  7  15  3  1  0
18  2  15  7  10  2  1  1
19  3  15  7  6  4  1  2
20  4  15  7  7  1  0  3
21  1  15  10  15  3  1  0
22  2  15  10  10  1  0  1
(22 rows)
 Example 3:
Manually assigned vertex combinations.
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edges',
'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
seq  path_seq  start_vid  end_vid  node  edge  cost  agg_cost
+++++++
1  1  6  7  6  4  1  0
2  2  6  7  7  1  0  1
3  1  6  10  6  4  1  0
4  2  6  10  7  8  1  1
5  3  6  10  11  9  1  2
6  4  6  10  16  16  1  3
7  5  6  10  15  3  1  4
8  6  6  10  10  1  0  5
9  1  12  10  12  13  1  0
10  2  12  10  17  15  1  1
11  3  12  10  16  16  1  2
12  4  12  10  15  3  1  3
13  5  12  10  10  1  0  4
(13 rows)
See Also¶
Indices and tables